Methods and devices for predictive coding of point clouds

ABSTRACT

Methods and devices for encoding a point cloud. A bit sequence signaling an occupancy pattern for sub-volumes of a volume is coded. Predictive coding is used to find a set of predicted points, from which a corresponding predicted occupancy pattern may be determined. The search for and selection of a coding mode for generating the set of predicted points may include a geometric distortion metric for evaluating how closely the geometry of the predicted set of points aligns with the geometry of the set of points to be coded. The geometric distortion metric may include a sum of absolute value distance between each point and its nearest predicted point. The metric may sum a logarithm of the distances to match more closely with coding rate cost.

FIELD

The present application generally relates to point cloud compressionand, in particular to methods and devices for predictive coding of pointclouds.

BACKGROUND

Data compression is used in communications and computer networking tostore, transmit, and reproduce information efficiently. There is anincreasing interest in representations of three-dimensional objects orspaces, which can involve large datasets and for which efficient andeffective compression would be highly useful and valued. In some cases,three-dimensional objects or spaces may be represented using a pointcloud, which is a set of points each having a three coordinate location(X, Y, Z) and, in some cases, other attributes like colour data (e.g.luminance and chrominance), transparency, reflectance, normal vector,etc. Point clouds can be static (a stationary object or a snapshot of anenvironment/object at a single point in time) or dynamic (a time-orderedsequence of point clouds).

Example applications for point clouds include topography and mappingapplications. Autonomous vehicle and other machine-vision applicationsmay rely on point cloud sensor data in the form of 3D scans of anenvironment, such as from a LiDAR scanner. Virtual reality simulationsmay rely on point clouds.

It will be appreciated that point clouds can involve large quantities ofdata and compressing (encoding and decoding) that data quickly andaccurately is of significant interest. Accordingly, it would beadvantageous to provide for methods and devices that more efficientlyand/or effectively compress data for point clouds.

In some cases of point cloud coding, it may be possible to exploitpredictive coding. The prediction may be used to predict point locationor attributes, and residual or error data may be encoded.

Nevertheless, a challenge remains in identifying and selecting asuitable geometric prediction. It would be advantageous to provide formethods and devices that code point cloud data using predictions thathave been selected with improved accuracy.

BRIEF DESCRIPTION OF THE DRAWINGS

Reference will now be made, by way of example, to the accompanyingdrawings which show example embodiments of the present application, andin which:

FIG. 1 shows a simplified block diagram of an example point cloudencoder;

FIG. 2 shows a simplified block diagram of an example point clouddecoder;

FIG. 3 shows an example partial sub-volume and associated tree structurefor coding;

FIG. 4 illustrates the recursive splitting and coding of an octree;

FIG. 5 shows an example scan pattern within an example cube from anoctree;

FIG. 6 shows an example occupancy pattern within an example cube;

FIG. 7 shows an example of neighbouring sub-volumes;

FIG. 8 shows an example neighbour configuration showing occupancy amongneighbouring nodes;

FIG. 9 illustrates the equivalence between non-binary coding andcascaded binary coding for an occupancy pattern;

FIG. 10 illustrates the generation of a predicted set of points based ona motion vector;

FIG. 11 diagrammatically shows an illustrative example of an iterativemotion vector search in two-dimensions;

FIG. 12 shows an example of largest prediction unit partitioning;

FIG. 13 shows an example of prediction unit split and occupancysignaling;

FIG. 14 shows a first example of part of a context-based entropy coder;

FIG. 15 shows a second example of part of a context-based entropy coder;

FIG. 16 shows a third example of part of a context-based entropy coder;

FIG. 17 shows an example simplified block diagram of an encoder; and

FIG. 18 shows an example simplified block diagram of a decoder.

Similar reference numerals may have been used in different figures todenote similar components.

DESCRIPTION OF EXAMPLE EMBODIMENTS

The present application describes methods of encoding and decoding pointclouds, and encoders and decoders for encoding and decoding pointclouds.

In one aspect, the present application describes method of encoding apoint cloud to generate a bitstream of compressed point cloud data, thepoint cloud being located within a volumetric space containing thepoints of the point cloud, each of the points having a geometriclocation within the volumetric space, wherein a sub-volume within thevolumetric space contains a set of points the locations of which areto-be-coded. The method includes determining a plurality of candidatecoding modes, wherein each candidate coding mode transforms a set ofpreviously-coded points into a candidate predicted set of points;selecting a coding mode from among the plurality of candidate codingmodes using rate-distortion optimization, where the rate-distortionoptimization includes, for one of the candidate coding modes,determining a geometric distortion between the set of points and thecandidate predicted set of points produced by said one of the candidatecoding modes, and wherein the geometric distortion is determined basedon a sum of the absolute distance between each point in the set ofpoints and a respective nearest predicted point in said candidatepredicted set of points; and coding the set of points partly based onthe predicted set of points determined by the selected coding mode, togenerate the bitstream.

In some implementations, the coding mode may include a motion vectordefining a translation of the set of previously-coded points to generatethe candidate predicted set of points.

In some implementations, the geometric distortion may be determinedbased on a sum of a non-linear function of the absolute distance betweeneach point and its respective nearest predicted point in said candidatepredicted set of points.

In some implementations, the geometric distortion may be determinedbased on a sum of a logarithm of the absolute distance between eachpoint and its respective nearest predicted point in said candidatepredicted set of points. In some such cases, the geometric distortion,D, may be determined in accordance with the expression:

$D = {\sum\limits_{\beta \in B}{\log_{2}\left( {1 + {\min\limits_{\varphi \in P}{{\beta - \varphi}}_{1}}} \right)}}$where B is the set of points in the volume, β is a point in the set ofpoints in the volume, P is the predicted set of points, and φ is therespective nearest predicted point to the point β in the set of points.

In some implementations, the respective nearest predicted point to eachpoint in the set of points is determined by finding, for a particularpoint in the set of points, a predicted point in the set of predictedpoints that has an L1 distance from the particular point.

In some implementations, selecting a coding mode may include performinga multi-round iterative search for a locally-best coding mode within asearch range, and each successive round of the search may includedetermining two or more locally-best coding modes and definingsuccessive new search ranges centered around respective pointsidentified by said locally-best coding modes. In some cases, themulti-round search determining two or more locally-best coding modes mayinclude calculating, for each candidate coding mode in a particularround, a rate-distortion expression that includes the geometricdistortion attributable to that candidate coding mode, and identifyingtwo or more locally least-cost coding modes for that particular round.

In some implementations, coding the set of points may includecontext-based entropy coding the set of points using context selectionbased, at least in part, on the predicted set of points.

In some implementations, the set of previously-coded points arepreviously-coded points from the point cloud located in a second volumepositioned proximate the volume.

In some implementations, the set of previously-coded points are from asecond point cloud temporally-related to the point cloud.

In some implementations, wherein the volumetric space is recursivelypartitioned and one of the partitions is the sub-volume.

In a further aspect, the present application describes encoders anddecoders configured to implement such methods of encoding and decoding.

In yet a further aspect, the present application describesnon-transitory computer-readable media storing computer-executableprogram instructions which, when executed, cause one or more processorsto perform the described methods of encoding and/or decoding.

In yet another aspect, the present application describes acomputer-readable signal containing program instructions which, whenexecuted by a computer, cause the computer to perform the describedmethods of encoding and/or decoding.

Other aspects and features of the present application will be understoodby those of ordinary skill in the art from a review of the followingdescription of examples in conjunction with the accompanying figures.

Any feature described in relation to one aspect or embodiment of theinvention may also be used in respect of one or more otheraspects/embodiments. These and other aspects of the present inventionwill be apparent from, and elucidated with reference to, the embodimentsdescribed herein.

At times in the description below, the terms “node”, “volume” and“sub-volume” may be used interchangeably. It will be appreciated that anode is associated with a volume or sub-volume. The node is a particularpoint on the tree that may be an internal node or a leaf node. Thevolume or sub-volume is the bounded physical space that the noderepresents. The term “volume” may, in some cases, be used to refer tothe largest bounded space defined for containing the point cloud. Avolume may be recursively divided into sub-volumes for the purpose ofbuilding out a tree-structure of interconnected nodes for coding thepoint cloud data.

In the present application, the term “and/or” is intended to cover allpossible combinations and sub-combinations of the listed elements,including any one of the listed elements alone, any sub-combination, orall of the elements, and without necessarily excluding additionalelements.

In the present application, the phrase “at least one of . . . or . . . ”is intended to cover any one or more of the listed elements, includingany one of the listed elements alone, any sub-combination, or all of theelements, without necessarily excluding any additional elements, andwithout necessarily requiring all of the elements.

A point cloud is a set of points in a three-dimensional coordinatesystem. The points are often intended to represent the external surfaceof one or more objects. Each point has a location (position) in thethree-dimensional coordinate system. The position may be represented bythree coordinates (X, Y, Z), which can be Cartesian or any othercoordinate system. The points may have other associated attributes, suchas colour, which may also be a three component value in some cases, suchas R, G, B or Y, Cb, Cr. Other associated attributes may includetransparency, reflectance, a normal vector, etc., depending on thedesired application for the point cloud data.

Point clouds can be static or dynamic. For example, a detailed scan ormapping of an object or topography may be static point cloud data. TheLiDAR-based scanning of an environment for machine-vision purposes maybe dynamic in that the point cloud (at least potentially) changes overtime, e.g. with each successive scan of a volume. The dynamic pointcloud is therefore a time-ordered sequence of point clouds.

Point cloud data may be used in a number of applications, includingconservation (scanning of historical or cultural objects), mapping,machine vision (such as autonomous or semi-autonomous cars), and virtualreality systems, to give some examples. Dynamic point cloud data forapplications like machine vision can be quite different from staticpoint cloud data like that for conservation purposes. Automotive vision,for example, typically involves relatively small resolution,non-coloured, highly dynamic point clouds obtained through LiDAR (orsimilar) sensors with a high frequency of capture. The objective of suchpoint clouds is not for human consumption or viewing but rather formachine object detection/classification in a decision process. As anexample, typical LiDAR frames contain on the order of tens of thousandsof points, whereas high quality virtual reality applications requireseveral millions of points. It may be expected that there will be ademand for higher resolution data over time as computational speedincreases and new applications are found.

While point cloud data is useful, a lack of effective and efficientcompression, i.e. encoding and decoding processes, may hamper adoptionand deployment. A particular challenge in coding point clouds that doesnot arise in the case of other data compression, like audio or video, isthe coding of the geometry of the point cloud. Point clouds tend to besparsely populated, which makes efficiently coding the location of thepoints that much more challenging.

One of the more common mechanisms for coding point cloud data is throughusing tree-based structures. In a tree-based structure, the boundingthree-dimensional volume for the point cloud is recursively divided intosub-volumes. Nodes of the tree correspond to sub-volumes. The decisionof whether or not to further divide a sub-volume may be based onresolution of the tree and/or whether there are any points contained inthe sub-volume. A leaf node may have an occupancy flag that indicateswhether its associated sub-volume contains a point or not. Splittingflags may signal whether a node has child nodes (i.e. whether a currentvolume has been further split into sub-volumes). These flags may beentropy coded in some cases and in some cases predictive coding may beused.

A commonly-used tree structure is an octree. In this structure, thevolumes/sub-volumes are all cubes and each split of a sub-volume resultsin eight further sub-volumes/sub-cubes. Another commonly-used treestructure is a KD-tree, in which a volume (cube or rectangular cuboid)is recursively divided in two by a plane orthogonal to one of the axes.Octrees are a special case of KD-trees, where the volume is divided bythree planes, each being orthogonal to one of the three axes. Both theseexamples relate to cubes or rectangular cuboids; however, the presentapplication is not restricted to such tree structures and the volumesand sub-volumes may have other shapes in some applications. Thepartitioning of a volume is not necessarily into two sub-volumes(KD-tree) or eight sub-volumes (octree), but could involve otherpartitions, including division into non-rectangular shapes or involvingnon-adjacent sub-volumes.

The present application may refer to octrees for ease of explanation andbecause they are a popular candidate tree structure for automotiveapplications, but it will be understood that the methods and devicesdescribed herein may be implemented using other tree structures.

Reference is now made to FIG. 1, which shows a simplified block diagramof a point cloud encoder 10 in accordance with aspects of the presentapplication. The point cloud encoder 10 includes a tree building module12 for receiving point cloud data and producing a tree (in this example,an octree) representing the geometry of the volumetric space containingpoint cloud and indicating the location or position of points from thepoint cloud in that geometry.

The basic process for creating an octree to code a point cloud mayinclude:

-   -   1. Start with a bounding volume (cube) containing the point        cloud in a coordinate system    -   2. Split the volume into 8 sub-volumes (eight sub-cubes)    -   3. For each sub-volume, mark the sub-volume with 0 if the        sub-volume is empty, or with 1 if there is at least one point in        it    -   4. For all sub-volumes marked with 1, repeat (2) to split those        sub-volumes, until a maximum depth of splitting is reached    -   5. For all leaf sub-volumes (sub-cubes) of maximum depth, mark        the leaf cube with 1 if it is non-empty, 0 otherwise

The above process might be described as an occupancy-equals-splittingprocess, where splitting implies occupancy, with the constraint thatthere is a maximum depth or resolution beyond which no further splittingwill occur. In this case, a single flag signals whether a node is splitand hence whether it is occupied by at least one point, and vice versa.At the maximum depth, the flag signals occupancy, with no furthersplitting possible.

In some implementations, splitting and occupancy are independent suchthat a node may be occupied and may or may not be split. There are twovariations of this implementation:

-   -   1. Split-then-occupied. A signal flag indicates whether a node        is split. If split, then the node must contain a point—that is        splitting implies occupancy. Otherwise, if the node is not to be        split then a further occupancy flag signals whether the node        contains at least one point. Accordingly, when a node is not        further split, i.e. it is a leaf node, the leaf node must have        an associated occupancy flag to indicate whether it contains any        points.    -   2. Occupied-then-split. A single flag indicates whether the node        is occupied. If not occupied, then no splitting occurs. If it is        occupied, then a splitting flag is coded to indicate whether the        node is further split or not.

Irrespective of which of the above-described processes is used to buildthe tree, it may be traversed in a pre-defined order (breadth-first ordepth-first, and in accordance with a scan pattern/order within eachdivided sub-volume) to produce a sequence of bits from the flags(occupancy and/or splitting flags). This may be termed the serializationor binarization of the tree. As shown in FIG. 1, in this example, thepoint cloud encoder 10 includes a binarizer 14 for binarizing the octreeto produce a bitstream of binarized data representing the tree.

This sequence of bits may then be encoded using an entropy encoder 16 toproduce a compressed bitstream. The entropy encoder 16 may encode thesequence of bits using a context model 18 that specifies probabilitiesfor coding bits based on a context determination by the entropy encoder16. The context model 18 may be adaptively updated after coding of eachbit or defined set of bits. The entropy encoder 16 may, in some cases,be a binary arithmetic encoder. The binary arithmetic encoder may, insome implementations, employ context-adaptive binary arithmetic coding(CABAC). In some implementations, coders other than arithmetic codersmay be used.

In some cases, the entropy encoder 16 may not be a binary coder, butinstead may operate on non-binary data. The output octree data from thetree building module 12 may not be evaluated in binary form but insteadmay be encoded as non-binary data. For example, in the case of anoctree, the eight flags within a sub-volume (e.g. occupancy flags) intheir scan order may be considered a 2⁸−1 bit number (e.g. an integerhaving a value between 1 and 255 since the value 0 is not possible for asplit sub-volume, i.e. it would not have been split if it was entirelyunoccupied). This number may be encoded by the entropy encoder using amulti-symbol arithmetic coder in some implementations. Within asub-volume, e.g. a cube, the sequence of flags that defines this integermay be termed a “pattern”.

Like with video or image coding, point cloud coding can includepredictive operations in which efforts are made to predict the locationof points in a volume. From the predicted locations of points, one canpredict the occupancy pattern for a sub-volume. Predictions may bespatial (dependent on previously coded sub-volumes in the same pointcloud) or temporal (dependent on previously coded point clouds in atime-ordered sequence of point clouds).

A block diagram of an example point cloud decoder 50 that corresponds tothe encoder 10 is shown in FIG. 2. The point cloud decoder 50 includesan entropy decoder 52 using the same context model 54 used by theencoder 10. The entropy decoder 52 receives the input bitstream ofcompressed data and entropy decodes the data to produce an outputsequence of decompressed bits. The sequence is then converted intoreconstructed point cloud data by a tree reconstructor 56. The treereconstructor 56 rebuilds the tree structure from the decompressed dataand knowledge of the scanning order in which the tree data wasbinarized. The tree reconstructor 56 is thus able to reconstruct thelocation of the points from the point cloud (subject to the resolutionof the tree coding).

An example partial sub-volume 100 is shown in FIG. 3. In this example, asub-volume 100 is shown in two-dimensions for ease of illustration, andthe size of the sub-volume 100 is 16×16. It will be noted that thesub-volume has been divided into four 8×8 sub-squares, and two of thosehave been further subdivided into 4×4 sub-squares, three of which arefurther divided to 2×2 sub-squares, and one of the 2×2 sub-square isthen divided into 1×1 squares. The 1×1 squares are the maximum depth ofthe tree and represent the finest resolution for positional point data.The points from the point cloud are shown as dots in the figure.

The structure of the tree 102 is shown to the right of the sub-volume100. The sequence of splitting flags 104 and the corresponding sequenceof occupancy flags 106, obtained in a pre-defined breadth-first scanorder, is shown to the right of the tree 102. It will be observed thatin this illustrative example, there is an occupancy flag for eachsub-volume (node) that is not split, i.e. that has an associatedsplitting flag set to zero. These sequences may be entropy encoded.

Another example, which employs an occupied ≡ splitting condition, isshown in FIG. 4. FIG. 4 illustrates the recursive splitting and codingof an octree 150. Only a portion of the octree 150 is shown in thefigure. A FIFO 152 is shown as processing the nodes for splitting toillustrate the breadth-first nature of the present process. The FIFO 152outputs an occupied node 154 that was queued in the FIFO 152 for furthersplitting after processing of its parent node 156. The tree buildersplits the sub-volume associated with the occupied node 154 into eightsub-volumes (cubes) and determines their occupancy. The occupancy may beindicated by an occupancy flag for each sub-volume. In a prescribed scanorder, the flags may be referred to as the occupancy pattern for thenode 154. The pattern may be specified by the integer representing thesequence of occupancy flags associated with the sub-volumes in thepre-defined scan order. In the case of an octree, the pattern is aninteger in the range [1, 255].

The entropy encoder then encodes that pattern using a non-binaryarithmetic encoder based on probabilities specified by the contextmodel. In this example, the probabilities may be a pattern distributionbased on an initial distribution model and adaptively updated. In oneimplementation, the pattern distribution is effectively a counter of thenumber of times each pattern (integer from 1 to 255) has beenencountered during coding. The pattern distribution may be updated aftereach sub-volume is coded. The pattern distribution may be normalized, asneeded, since the relative frequency of the patterns is germane to theprobability assessment and not the absolute count.

Based on the pattern, those child nodes that are occupied (e.g. have aflag=1) are then pushed into the FIFO 152 for further splitting in turn(provided the nodes are not a maximum depth of the tree).

Reference is now made to FIG. 5, which shows an example cube 180 from anoctree. The cube 180 is subdivided into eight sub-cubes. The scan orderfor reading the flags results in an eight bit string, which can be readas an integer [1, 255] in binary. Based on the scan order and theresulting bit position of each sub-cube's flag in the string, thesub-cubes have the values shown in FIG. 5. The scan order may be anysequence of the sub-cubes, provided both the encoder and decoder use thesame scan order.

As an example, FIG. 6 shows the cube 180 the number of probabilitydistributions may equal in which the four “front” sub-cubes areoccupied. This would correspond to pattern 85, on the basis that thesub-cubes occupied are cubes 1+4+16+64. The integer pattern numberspecifies the pattern of occupancy in the sub-cubes.

In European patent application no. 18305037.6, the present applicantsdescribed methods and devices for selecting among available patterndistributions to be used in coding a particular node's pattern ofoccupancy based on some occupancy information from previously-codednodes near the particular node. In one example implementation, theoccupancy information is obtained from the pattern of occupancy of theparent to the particular node. In another example implementation, theoccupancy information is obtained from one or more nodes neighbouringthe particular node. The contents of European patent application no.18305037.6 are incorporated herein by reference. This is referred to asdetermining a “neighbour configuration”, and selecting a context (i.e. apattern distribution) at least partly based on the neighbourconfiguration.

FIG. 7 illustrates a set of neighbors surrounding a current node, whereneighbour is defined as nodes sharing a face. In this example, thenodes/sub-volumes are cubes and the cube at the center of the image hassix neighbours, one for each face. In an octree, it will be appreciatedthat neighbours to the current node will include three sibling nodes. Itwill also include three nodes that do not have the same parent node.Accordingly, occupancy data for some of the neighboring nodes will beavailable because they are siblings, but occupancy data for someneighbouring nodes may or may not be available, depending on whetherthose nodes were previously coded. Special handling may be applied todeal with missing neighbours. In some implementations, the missingneighbour may be presumed to be occupied or may be presumed to beunoccupied. It will be appreciated that the neighbour definition may bebroadened to include neighbouring nodes based on a shared edge or basedon a shared vertex to include additional adjacent sub-volumes in theassessment.

The occupancy of the neighbours may be read in a scan order thateffectively assigns a value to each neighbour, much like as is describedabove with respect to occupancy patterns. As illustrated, theneighbouring nodes effectively take values of 1, 2, 4, 8, 16 or 32, andthere are therefore 64 (0 to 63) possible neighbour occupancyconfigurations. This value may be termed the “neighbour configuration”herein. As an example, FIG. 8 illustrates an example of neighbourconfiguration 15, in which neighbours 1, 2, 4 and 8 are occupied andneighbours 16 and 32 are empty.

In some cases, the number of probability distributions may equal thenumber of possible occupancy outcomes in the selection criteria. Inother words, in the case of a parent pattern for an octree, there wouldbe probability distributions involving 255 probabilities each. In thecase of neighbour configuration, if neighbour is defined as sharing aface, there would be 64 probability distributions. However, it will beunderstood that too many distributions may result in slow adaptation dueto scarcity of data, i.e. context dilution. Accordingly, in someembodiments, similar patterns may be grouped so as to use the sameprobability distribution. For example separate distributions may be usedfor patterns corresponding to fully occupied, vertically-oriented,horizontally-oriented, mostly empty, and then all other cases. Thiscould reduce the number of probability distributions to about five. Itwill be appreciated that different groupings of patterns could be formedto result in a different number of probability distributions.

In one variation to the neighbour-based probability distributionselection, the number of distributions may be reduced by exploiting thesymmetry of the neighbourhood. By permuting the neighbour configurationor permuting the pattern distribution, structurally similarconfigurations having a line of symmetry can re-use the samedistribution. As a result, the number of neighbour configurations (andthus distribution patterns), may be reduced. In some cases, the 64neighbour configurations can be reduced using these techniques to 64,24, 18 or 10 total neighbour configurations. In other words, neighbourconfigurations that can use the same pattern distribution may be groupedinto a class. A class containing more than one neighbour configurationmay be referred to herein as a “neighbour configuration” in that one ofthe neighbour configurations effectively subsumes other neighbourconfigurations by way of reflection or permutation of those otherconfigurations.

The above-described techniques of using neighbour occupancy informationfor coding tree occupancy focus on using non-binary entropy coding ofthe occupancy pattern, where a pattern distribution is selected based onneighbour occupancy information, i.e. neighbour configuration. However,in some instances, the use of binary coders can be more efficient interms of hardware implementation. Moreover, on-the-fly updates to manyprobabilities may require fast-access memory and computation within theheart of the arithmetic coder. Accordingly, it may be advantageous tofind methods and devices for entropy encoding the occupancy patternusing binary arithmetic coders. It would be advantageous to use binarycoders if it can be done without significantly degrading compressionperformance and while guarding against having an overwhelming number ofcontexts to track.

The use of binary coders in place of a non-binary coder is reflected inthe entropy formula:H(X ₁ ,X ₂ |Y)=H(X ₁ |Y)H(X ₂ |Y,X ₁)

where X=(X₁, X₂) is the non-binary information to be coded, and Y is thecontext for coding, i.e. the neighbour configuration or selected patterndistribution. To convert non-binary coding of X into binary coding, theinformation (X₁, X₂) is split into information X₁ and X₂ that can becoded separately without increasing the entropy. To do so, one must codeone of the two depending on the other, here X₂ depending on X₁. This canbe extended to n bits of information in X. For example, for n=3:H(X ₁ ,X ₂ ,X ₃ |Y)=H(X ₁ |Y)H(X ₂ |Y,X ₁)H(X ₃ |Y,X ₁ ,X ₂)

It will be understood that as the occupancy pattern, i.e. bit sequenceX, gets longer there are more conditions for coding later bits in thesequence. For a binary coder (e.g. CABAC) this means a large increase inthe number of contexts to track and manage. Using an octree as anexample, where the occupancy pattern is an eight-bit sequence b=b₀ . . .b₇, the bit sequence may be split into the eight binary information bitsb₀ . . . b₇. The coding may use the neighbour configuration N (or NC)for determining context. Assuming that we can reduce the neighbourconfigurations to 10 effective neighbour configurations through groupingof neighbour configurations into classes of invariance, as describedabove, then N is an integer belonging to {0, 1, 2, . . . , 9}. Forshorthand, the “classes of invariant neighbour configurations” may bereferred to herein, at times, simply as the “neighbour configurations”,although it will be appreciated that this reduced number of neighbourconfigurations may be realized based on the class-based grouping ofneighbour configurations based on invariance.

FIG. 9 illustrates the splitting of an eight-bit pattern or sequenceinto eight individual bits for binary entropy coding. It will be notedthat the first bit of the sequence is encoded based on the neighbourconfiguration, so there are ten total contexts available. The next bitof the sequence is encoded based on the neighbour configuration and anypreviously-encoded bits, i.e. bit b₀. This involves 20 total availablecontexts: obtained as the product of 10 from N and 2 from b₀. The finalbit, b₇, is entropy encoded using a context selected from 1280 availablecontexts: obtained as the product of 10 from N and 128 from the partialpattern given by the previously-encoded bits b₀, . . . , b₆. That is,for each bit the number of contexts (i.e. possible combinations ofconditions/dependencies) is the product of the number of neighbourconfigurations defined (10, in this example, based on grouping of the 64neighbour configurations into classes), and the number of partialpatterns possible from the ordered sequence of n−1 previously-encodedbits (given by 2^(n−1)).

As a result, there are a total of 2550 contexts to maintain inconnection with binary coding of the occupancy pattern. This is anexcessively large number of contexts to track, and the relative scarcitymay cause poor performance because of context dilution, particularly forlater bits in the sequence.

Accordingly, in some cases the encoders and decoders that determinewhether the set of contexts can be reduced and, if so, apply a contextreduction operation to realize a smaller set of available contexts forentropy coding at least part of an occupancy pattern using a binarycoder. In at least some implementations, the context reduction isapplied a priori to realize a reduced or smaller set of contexts thatare then used by the encoder and decoder based on determining that thecontext reduction conditions are met. Those conditions may includedetermining that a neighbour configuration is empty or full, or that thebit being coded is at or above a particular position in the bitsequence, for example.

The context reduction operation reduces the number of available contextsin a set of available contexts to a smaller set containing fewer totalcontexts. It will be recalled, that the number of available contexts maydepend, in part, on the bit position in the sequence, i.e. the index,since the context may depend on a partial pattern of previously-codedbits from the bits sequence. In some implementations, the number ofcontexts available in the set, before reduction, may be based on thenumber of neighbour configurations multiplied by the number of partialpatterns possible with the previously-coded bits. For a bit at index i,where i ranges from 0 to n, the number of partial patterns may be givenby 2′.

Example context reduction operations include reducing neighbourconfigurations for later bits in the bit sequence on the basis thatpreviously-coded bits are associated with sub-volumes that screen orshield one of the neighbouring volumes, meaning the occupancy dataprovided by the previously-coded bits is more significant and relevantthan the occupancy data associated with the shielded volume. Anotherexample context reduction involves special handling of cases such asempty neighbour configurations or completely full neighbourconfigurations. Such situations may indicate a lack of directionalityand, thus, less need to take into account the order of previously-codedbits associated with the sub-volumes. Finally, an example contextreduction operation is applying a mapping of a set of contexts to asmaller set of contexts based on determining statistical similaritiesbetween pairs of contexts. The statistical similarities may be based ona distance metric between the pairs of contexts. Any such contextreduction operations may be used individually or together in combinationor sub-combination in some cases to reduce then number of contextsavailable for binary entropy coding at least some of the bits of anoccupancy pattern.

Prediction in Occupancy Coding

As noted earlier, point cloud coding may involve the use of predictivecoding. As will be familiar from video coding, predictive coding mayinclude inter-prediction, where points for a sub-volume in the pointcloud are predicted from the points of a previously-coded point cloudwith high temporal correlation, or intra-prediction, where points forthe sub-volume are predicted from previously-coded nearby points in thesame point cloud. In either case, the previously-coded points are usedto build a set of predicted points within the same geometric space asthe sub-volume. With intra-prediction, a local plane estimation may beused to obtain a predicted set of points.

In video, prediction is understood as building a block of predictedpixels located in exactly the same spot as the block of pixels beingcoded. That is there is a one-to-one pixel-to-predicted-pixelcorrespondence, and the prediction attempts to predict the colour (e.g.Y, Cr, Cb). Intra-coding builds a predicted block of predicted pixelsbased on the colour values of nearby previously-coded pixels and anintra-coding direction. Inter-coding builds a predicted block by findinga block in a temporally related frame and translating it to the locationof the current block based on a motion vector. Effectively, the motionvector identifies where to find the block in the related frame that willbe used as a predicted block. The colour values of the pixels in theblock in the related frame serve as the predicted colour values.

In the case of point cloud data, the prediction may be more complex. Thedata to be coded includes geometric location of points within a volume(and possibly other attributes, like colour). An inter-coding predictionbuilt from a temporally-related point cloud may be based on selecting avolume and translating and/or transforming that volume such that it ispositioned so as to subsume (i.e. contain) the space occupied by thevolume to-be-coded. Note that this does not necessarily result in aone-to-one point-to-predicted-point correspondence. Moreover, themovement of the volume of points may include both simple translation by3D motion vector and transformation(s). The transformations may includesolid transformations such as rotations, but could include non-solidtransformations/deformations. A general matrix formulation forgenerating a 3D prediction is given by:

$\begin{bmatrix}X^{\prime} \\Y^{\prime} \\Z^{\prime}\end{bmatrix} = {{\begin{bmatrix}* & * & * \\* & * & * \\* & * & *\end{bmatrix}\begin{bmatrix}X \\Y \\Z\end{bmatrix}} + \begin{bmatrix}V_{x} \\V_{y} \\V_{z}\end{bmatrix}}$

The motion vector V (V_(x), V_(y), V_(z)) gives a 3D translation,whereas the 3×3 matrix provides for possible transformation. If the 3×3matrix is zero, one has only 3D translation along the vector V. In thecase where the matrix is orthonormal, one obtains a solid transformationwithout local deformation of the set of points. A more general matrixallows for non-solid deformations.

Selecting a Coding Mode for Prediction

The more complex structure of point clouds, and the fact that aprediction may not have a one-to-one correspondence with the pointswithin the volume to-be-coded make selection of a suitable predictionmore difficult. To select a suitable prediction, the present applicationprovides, in one aspect, that a set of candidate coding modes are to beevaluated within a search range. Each candidate coding mode produces acandidate predicted set of points from a set of previously-coded points,where the candidate predicted set of points occupy a prediction volumewithin the 3D coordinate system. The coordinates of prediction volumeinclude the coordinates of the volume to-be-coded (in a simple case, theprediction volume matches the volume to-be-coded in size).

Selection of a candidate coding mode may rely on rate-distortionevaluation. The determination of rate cost may be relativelystraightforward, but the determination of distortion cannot be easilydetermined. Because a point-to-be-coded does not necessarily have acorresponding predicted point at the same location, colour distortion isdifficult to quantify. Moreover, it is not clear how to quantifydistortion in geometry.

In accordance, with one aspect of the present application, themeasurement of distortion between the set of predicted points within theprediction volume and the set of points to-be-coded in the currentvolume is based on a sum of absolute differences between each point ofthe set of points to-be-coded and its nearest predicted point. Thismetric may be suitable, based in part on how the prediction is to beused in coding, which is discussed further below.

Reference is now made to FIG. 10, which shows a search volume W ofpreviously-coded points of a point cloud. For the purposes of thepresent illustration, inter-coding may be presumed, such that the searchvolume W is with respect to the points in a point cloud at time T1. Thepoints to be coded, B, are from a point cloud at time T2 and are locatedin a volume positioned at a particular set of coordinates that fallwithin the coordinates of the search volume W (which may be centeredaround the location of the volume containing B in some implementations).The intersection of the volume and the point cloud defines the set ofpoints B. The volume may be referred to as a prediction unit in someinstances. Prediction units will be discussed further below.

A candidate coding mode M specifies a translation (and/ortransformation) that, when applied to the points in W results in arepositioning of the previously-coded points in accordance with thecoding mode. In this example, the coding mode M specifies a translationby three-dimensional vector V. The repositioned points are a candidateset of predicted points P. The candidate set of predicted points P is afunction of W and the candidate coding mode M: P(W,M). In this case, thecoding mode M is the vector V, so P(W,M)=P(W,V).

The distortion D(M)=D(B, P(W,M)) may be determined to assess how wellthe set of predicted points P(W, M) match up to the set of points Bwithin the volume. That distortion may be measured as:

${D\left( {B,P} \right)} = {\sum\limits_{\beta \in B}{\log_{2}\left( {1 + {\min\limits_{\varphi \in P}{{\beta - \varphi}}_{1}}} \right)}}$

where B is the set of points to be coded in the volume, β is a point inthe set of points B, and the notation β∈B indicates that the summationoccurs over all of the points to be coded in the volume. The notation corefers to a point in the candidate set of prediction points P. Thedistance to a nearest prediction point taken from the candidate set ofpredicted points P is calculated as:

$\min\limits_{\varphi \in P}{{\beta - \varphi}}_{1}$

where ∥•∥₁ stands for the L1 norm. In 3D coordinates (X, Y, Z), thedistance ∥β−φ∥₁ may be determined from the sum of absolute coordinatedifferences given by |β_(X)−φ_(X)|+|β_(Y)−φ_(Y)|+β_(Z)−φ_(Z)|. Anothernorm like the L2 norm may be used instead of the L1 norm, such as:∥β−φ∥₂ ²=|β_(X)−φ_(X)|²+|β_(Y)−φ_(Y)|² +|B _(Z)−φ_(Z)|²

The present application is not limited to a specific norm to compute thedistance between points β and φ, however it will be appreciated that theL1 norm may be computationally simpler to obtain than the L2 norm.

A base-2 logarithm assists in converting the error values to a valuecloser to the bitrate required to code the error, thus making thedistortion more compatible with the rate within the Lagrange costexpression of a rate-distortion optimization (RDO) process. Inapproximate terms, an error of 1 will require one bit for correction,whereas an error of 2^(N)−1 will require N bits for correction.Accordingly, the log₂ factor assists in improving the RDO process,particularly in the case of coding geometric data for an octree.

This distortion is a one-way distance of B relatively to P that valueszero if and only if B is included in P. Practically, distortionexpressed the other way, i.e. D(P,B), is not needed because it is likelythat the density of points of B is similar to the density of points ofP. Moreover, one-way distortion is much simpler and faster to calculatethat two-way distortion. In case B and P have the same number of points,and if the distortion D(B,P) is zero, then one has the equality B=P, andthe value D(P,B) is not needed to decide the equality.

In some other implementation, the distortion includes a sum ofnon-linear functions other than of the form log₂(1+x), where x is themagnitude of the geometric mismatch. For example, a logarithm other thana base-2 logarithm may be used in some cases. Instead of a logarithm, apower function may be used, such as x^(p), where p is less than 1, suchas a square root. Any selected non-linear function should evaluate tozero when the geometric mismatch is zero, since a perfect match implieszero distortion. In some cases, the non-linear function may be capped ata maximum value (a saturation limit) so that one very poorly predictedpoint does not overwhelm the distortion measurement. For example, theexpression may be g(x)=min (f(x), s), where s is the maximum.

As mentioned above, the identification of a “best” coding mode may bebased on a search and evaluation of candidate coding modes within asearch range. The search may, in some cases, be iterative. Although thismay result in selection of a local minimum rather than a globallyoptimized minimum, it may reduce the computational burden on theencoder. In such embodiments, the coding mode search is an iterativeprocess that converges to a local minimum, i.e. a “best” coding mode,that minimizes the RDO function locally.

As noted above, the coding mode in 3D point cloud prediction may includetranslation and transformation. For the purposes of the presentillustration and explanation, the coding mode will be presumed toinvolve translation without transformation. That is, the coding modespecifies a motion vector that indicates the location of a 3D volumewithin the search range W in the previously-coded portion of the pointcloud (or a temporally-related previously-coded point cloud). For theexample illustrated below, the search is presumed to be within atemporally related point-cloud.

The RDO function for finding the locally-optimal motion vector V in thisillustrative example may be expressed as:C(V)=D(B,P(W,V))+λR(V)

where C(V) is the RDO cost associated with vector V, which specifiespredicted set of points P(W, V) given search range W within thepreviously-coded points, and λ is the Lagrange parameter.

Accordingly, the vector V_(best) that minimizes the cost is obtained by:

${V_{best}(B)} = {{\underset{V}{argmin}\;{C(V)}} = {\underset{V}{argmin}{D\left( {B,{{P\left( {W,V} \right)} + {\lambda{R(V)}}}} \right)}}}$

Reference is now made to FIG. 11, which diagrammatically illustrates oneexample of an iterative search algorithm. For ease of explanation andillustration, the example is shown in 2-dimensions, but it will beappreciated that the operations and principles are easily extended to3-dimensions, or N-dimensions, in light of the description herein, whereN-dimensions may account for additional parameters.

In this example, the block containing the set of points B is presumed tobe a 3×3 block (or 3×3×3 in a 3D example, or 3^(N) in an N-dimensionalexample), and the iterative search centers around the geometric locationof the block (here labelled “B”) within a search space or range W. Afirst round 200 of the iterative search may begin with a set of coarsecandidate vectors 202 within the search space W. In this example, Thesearch includes the zero vector (V=0) and vectors pointing to 3×3 blockssurrounding the block containing B. Obviously other patterns may be usedin other embodiments and there may be fewer or more coarse candidatevectors 203. The first round 200 search patterns is a grid of pointsbased on a displacement D.

For each of the candidate vectors 202, the cost is determined inaccordance with an RDO expression, such as those shown above, and theN_(best) candidate vectors 202 are identified. In this example, N_(best)is set to three, such that in the first round 200, the three best (leastcost) candidate vectors 202 are identified, as indicated by the darkcircles on FIG. 11.

In the second round 204, the search is again conducted, but this timethere are three search ranges, each centered around the respectivepoints identified by the N_(best) candidate vectors from the first round200. The second round candidate vectors 206 include each of the N_(best)candidate vectors and vectors that point to a sub-grid centered at thepoint indicated by each N_(best) candidate vector. The sub-grid is basedon a displacement of D/2. The cost of each second round candidate vector206 is then determined and the N_(best) second round candidate vectors208 are kept.

This same process is repeated in a third round 210 in this example. Astopping condition, such as D=D_(min), results in a final set ofcandidate vectors from which the local best (least cost) candidatevector, V_(best), is selected. The number of iterations and the stoppingconditions may be modified to suit particular implementations. Thevector V_(best) identifies a block 212 (cuboid in 3D) ofpreviously-coded point data to be translated by −V_(best) to serve asthe set of predicted points P.

It will be appreciated that the selection process may be furtherimproved through including colour distortion as part of the costfunction, if colour is an attribute for the particular point cloud beingcoded. It will be appreciated that not all point clouds have colourattributes, and some have other attributes that may be incorporated inthe cost function in a manner similar to colour. To incorporate the costof colour distortion, a term E may be added to the RDO cost expression:C(V)=D(B,P(W,V))+μE(B,P(W,V))+λR(V)

The distortion E may be computed in the YCbCr colour space using theformula:

${E\left( {B,P} \right)} = {\sum\limits_{\beta \in B}{{{{YCbCr}(\beta)} - {YCb{{Cr}\left( {\varphi_{nearest}(\beta)} \right)}}}}_{1}}$

The nearest predicted point co in P to a point β in B may be defined as:

${\varphi_{nearest}(\beta)} = {\underset{\varphi \in P}{argmin}{{\beta - \varphi}}_{1}}$

The predicted colour error of a point β is defined as the colourdifference with the closest predicted point φ_(nearest)(β), and thedistortion is obtained by the sum over all points β of B. The colourdifference is preferably performed in the YCbCr space but may performedin other spaces like RGB, or on Y only. In another embodiment, thedifference may be weighted with a higher weight on the luma component Yrelatively to the two other components Cb and Cr.

A balancing parameter μ between geometry and colour distortions isintroduced to weight the distortion E. If μ=0, then there is no colourdistortion in the cost and the mode selection process targets optimalgeometry prediction without trying to optimize the colour prediction. Onthe other hand, if μ=∞ optimal colour prediction is targetedindependently on the geometric quality D and the bitrate.

A residual colour res(β) may be obtained by:res(β)=YCbCr(β)−YCbCr(φ_(nearest)(β))

In the above examples, it was presumed that the volume that contains theset of points B was known. Selecting a suitable volume for selecting theset of points B for which a prediction is to be generated is a furtherchallenge in predictive coding of point clouds.

Point clouds have a fundamental difference relatively to video where allpixels are occupied: points of a point cloud do not occupy the whole 3Dspace. On the contrary, the space is generally very sparsely occupied bythe points of the point cloud. Consequently, only parts of the spacethat are occupied by the current point clouds should be eligible toundergo a prediction. A global structure may be useful to signal theseeligible parts. In this regard, the concept of a 3D Largest PredictionUnit (LPU) may be introduced.

In general, a 3D space may be partitioned into LPUs, inside of whichlocal prediction modes (coding modes) may be selected. For simplicity,LPUs in this example may be 3D cuboids obtained from a regular gridpartitioning of the 3D space. An LPU that contains at least one point ofthe point cloud is a populated LPU and an LPU that contains no points ofthe point cloud is a non-populated LPU.

A flag may be used to signal whether or not each LPU is populated.However, this may lead to many flags to encode and, in order to improvecompression, these flags may be inferred by the collocated LPU of areference frame and/or neighbouring LPUs of the current frame, in someembodiments.

Depending on the local topology, a LPU may be too big to adequatelyobtain a prediction of the points belonging to it. Thus, it may beadvantageous to split a LPU into smaller Prediction Units (PUs). Thedetermination of whether to split an LPU into smaller PUs may be builtinto the RDO-based coding mode selection process. A flag may indicatewhether a PU is further split for any PU that is populated, unless itmay be inferred to be split/not-split based on side information. Forexample, maximum split depth may imply “not split”.

FIG. 12 shows, in 2D form for simplicity, the various 1^(st) and 2^(nd)order splitting of an LPU into PUs. An example of splitting/occupancyflags for an illustrative 2-D embodiment is shown in FIG. 13.

The cost of coding the PU tree may further be incorporated into the costfunction for the RDO-based search process. To select the best PUstructure during the competitive process, the encoder may use theadditive property of the costs. Individual PU costs are summed togetherwith the PU tree associated rate to obtain the total cost of a LPU. TheLPU structure, together with its associated modes, having the least costmay be selected as the best structure.

Many of the above examples involve tree-based coding of the point cloudgeometry. It will understood that the above-described processes forselecting a suitable prediction may be applied in the case of otherpoint cloud geometry coding techniques. For example, image based methodscode the geometry in depth maps. Predictive coding may be used bygenerating a prediction between 2D blocks of depth maps (e.g. a currentdepth map to be coded and a reference depth map). The metric fordetermining distortion in calculating the RDO cost may be computed in 3Dafter de-projection of the two 2D blocks to obtain two 3D sets (B and P)of points. This permits the use of the above-described 3D geometricdistortion metric in determining or selecting a coding mode forgenerating a predicted depth map.

Using a Prediction to Improve Compression of Point Cloud Data

In some implementations, a prediction may be used to generate apredicted occupancy of a node of an octree. The residual between thepredicted occupancy pattern and the actual occupancy pattern may then beencoded; however, this technique does not mesh well with theimprovements to context selection based on neighbouring volumes(neighbour configuration) and/or previously-encoded bits of the bitssequence, both of which are based on exploiting non-randomdirectionality in the occupancy pattern.

Accordingly, in another aspect, the present application proposes methodsand device for using point cloud predictions to improve thecontext-based coding process through improved context selection forcoding the actual occupancy patterns. In some embodiments, the coding isbinary entropy coding.

The contexts for coding the occupancy pattern may be subdivided into twoor more subsets of contexts. In one example implementation, when codingan occupancy pattern for a sub-volume and selecting a context forcoding, the context selection uses a first subset if the predictionindicates that the sub-volume contains no predicted points and uses asecond subset if the prediction indicates that the sub-volume containsat least one predicted point. The coding may include coding a bit of anoccupancy pattern in a binary entropy coder, in some examples.

Reference is now made to FIG. 14, which shows, in block diagram form,part of a first example of a context-based entropy coder 300 for use inencoding or decoding point cloud data. The context-based entropy coder300 generates a predicted set of points in accordance with a codingmode. The context-based entropy coder 300 may be used to code anoccupancy pattern, e.g. b₀ . . . b₇, associated with a volume that hasbeen subdivided into sub-volumes, where the occupancy pattern is a bitsequence where each bit b_(i) indicates the occupancy status of arespective one of the sub-volumes in a prescribed order within thevolume. The context-based entropy coder 300 may determine a predictedoccupancy pattern, e.g. bP₀ . . . bP₇, using the same volume/sub-volumepartitioning of the space, where the predicted occupancy pattern is abit sequence in which each bit bP_(i) indicates whether there is atleast one predicted point in a respective one of the sub-volumes in theprescribed order.

Rather than creating a residual by comparing the occupancy pattern tothe predicted occupancy pattern, e.g. using XOR, the context-basedentropy coder 300 uses the predicted occupancy pattern as the basis, atleast in part, for selecting a context for coding the occupancy pattern.In some cases, the predicted occupancy pattern is the basis forselecting between two or more context sets, and further information,such as neighbour configuration and/or previously-coded bits of theoccupancy pattern, serve as the basis for selecting a context fromwithin the selected context set.

In this example, the context-based entropy coder 300 first determineswhether the predicted occupancy pattern is empty. That is, whetherbP_(i)=0 for all i=0, . . . , 7. In such a case, there is effectively noprediction available with respect to the volume being coded, andprediction-based selection of contexts may be disabled for the coding ofthe occupancy pattern. As a result, in this case, the context-basedentropy coder may select contexts for coding the occupancy pattern usingwhatever non-predictive context-based selection process is implemented.This may include reference to neighbour configuration, previously-codedbits of the bit sequence, etc.

If the predicted occupancy pattern is not empty, then on a bit-by-bitbasis the context-based entropy coder 300 selects a context and codesthe occupancy pattern bits. In this regard, it may, for each bitdetermine whether the corresponding sub-volume contains at least onepredicted point, i.e. whether bP_(i) is non-zero. If bP_(i) is zero, itindicates that the corresponding sub-volume is predicted to be empty. Onthat basis the context-based entropy coder may select a first set ofcontexts, whereas if the prediction indicates that the sub-volume ispredicted to contain at least one predicted point, then thecontext-based entropy coder may select a second set of contexts. Contextselection within those respective sets may then occur for the bit b_(i)based on context selection criteria or conditions, such as neighbourconfiguration, previously-coded bits of the sequence, etc. In somecases, the context selection for a bit b_(i) from a set of availablecontexts is based on a combination of neighbour configuration,previously-coded bits of the occupancy pattern, and the predictedoccupancy pattern bit bP_(i), all of which are used to determine theindex to a set of contexts that selects the context for use in codingthe bit b_(i). Once the context for coding b_(i) has been determined,the bit bi is coded using an arithmetic coder.

Referring now to FIG. 15, another example of a context-based entropycoder 400 is shown. In this example, the entropy coder 400 uses thepredicted occupancy pattern bP to select between subsets of contexts. Ifthe predicted occupancy pattern is empty, the predictive contextselection feature is disabled for coding the occupancy pattern and thecoder 400 selects contexts using other criteria. The contexts may, insome embodiments, be selected from a first subset of contexts. If thepredicted occupancy pattern is not empty, then the entropy coder 400determines whether, for each bit b_(i) to be coded, the correspondingpredicted occupancy pattern bit bP_(i) is non-zero. If it is zero, thenthe corresponding sub-volume is predicted to be empty and a secondsubset of contexts may be used for coding the bit b_(i). If thepredicted occupancy pattern bit bP_(i) is non-zero, then the sub-volumeis predicted to contain at least one point. In this example, the entropycoder 400 then assesses how many predicted points are found with thecorresponding sub-volume. If the number of predicted points in thesub-volume does not exceed a preset threshold value, then the sub-volumeis predicted to be occupied but sparsely populated and a third subset ofcontexts is used for coding. If the number of predicted points in thesub-volume exceeds the preset threshold value, then the sub-volume ispredicted to be densely populated with points and a fourth subset ofcontexts is then used for selecting a context for coding b_(i).

The preset threshold value may be set to any number that signals adensely populated sub-volume. Tuning of the preset threshold value maytake place using test sequences to identify a value that best results incompression improvements through context selection for occupiedsub-volumes.

In yet a further example implementation, the entropy coder 400 may havemore than one preset threshold value against which the count ofpredicted points within the sub-volume is compared, and which is used asthe basis for selecting a subset of contexts for coding the occupancypattern bit b_(i).

It will be appreciated that the present context selection processdescribed in the above examples integrates well with other contextselection processes, whether they involve neighbour configuration,previously-coded occupancy pattern bits, or context reductionoperations.

Reference is now made to FIG. 16, which shows a further example of partof a context-based entropy coder 500. The context-based entropy coder500 uses the same process described above with regard to the secondexample context-based entropy coder 400, but in this case includes aconditional prediction deactivation operation. It may be that someregions of the point cloud are well predicted and some portions arepoorly predicted. It may be possible to evaluate the likely predictionquality locally by looking at the quality that was realized for parentnodes, i.e. at a larger scale of coding. If the prediction turned out tobe rather poor for a parent node, then the prediction for child nodes isalso likely to be poor. On this basis, the entropy coder 500 maydetermine that prediction is not to be used for those child nodes.

A determination of the “quality” of a prediction may be made based thenumber of bits in an occupancy pattern that were incorrectly predicted,i.e. count how many sub-volumes were incorrectly predicted to beoccupied or unoccupied. This count, N_(wrong), may be determined as:N _(wrong) =#{j|bP _(j) !=b _(j)}

The count of incorrectly predicted sub-volumes is then compared to a setthreshold N_(bad) and the node will be deemed “poorly predicted” ifN_(wrong)≥N_(bad). In one illustrative example based on octreepartitioning, N_(bad) may be set to 4, although it will be understoodthat it may be set to other values.

Accordingly, when starting the coding of an occupancy pattern b₀, . . .b₇ for a volume/node, the entropy coder 500 first evaluates whether itsparent volume/node was poorly predicted or not. If it was not poorlypredicted, then the entropy coder 500 uses prediction-based contextselection (subject to possibly disabling it if the predicted occupancypattern is empty) in coding the current node's occupancy pattern.

It will be appreciated that the above examples of entropy coders eachuse the predicted occupancy pattern as the basis for context selection.Moreover, in some of the examples, the predicted occupancy pattern isused as the basis for context set selection for coding a bit b_(i) ofthe occupancy pattern dependent on whether the corresponding predictedoccupancy bit is non-zero. In some cases, the count of predicted pointswithin a sub-volume is also used as the basis for context set selectionor context selection.

Impact on Compression Performance

The use of 10 neighbour configurations and non-binary coding provides acompression gain over current implementations of the MPEG test model forpoint cloud coding. The use of 10 neighbour configurations with cascadedbinary coding using 2550 contexts results in an even better improvementin compression efficiency. When using context reduction to reduce thetotal number of contexts to 576 the binary coding compression is stillmarginally better than implementation using non-binary coding, and muchbetter than the test model.

The use of prediction in improving context selection shows a yet furthersignificant improvement in compression efficiency. Using a movingvehicle point cloud, coding using context-reduced neighbour-based codingshowed an average of about 9% compression improvement over the testmodel, whereas motion compensation using an implementation of the motionvector search process described above results in a 23% gain incompression efficiency over the test model. This may be compared to amotion compensation implementation with no search and using a motionvector V=0 (basing the prediction on a co-located sub-volume of atemporally-related point cloud) that provides a 13% improvement over thetest model. With computer-graphics-based virtual-reality test pointclouds, the improvement is more marked at over 50% for prediction-basedcoding involving a motion vector search.

Reference is now made to FIG. 17, which shows a simplified block diagramof an example embodiment of an encoder 1100. The encoder 1100 includes aprocessor 1102, memory 1104, and an encoding application 1106. Theencoding application 1106 may include a computer program or applicationstored in memory 1104 and containing instructions that, when executed,cause the processor 1102 to perform operations such as those describedherein. For example, the encoding application 1106 may encode and outputbitstreams encoded in accordance with the processes described herein. Itwill be understood that the encoding application 1106 may be stored on anon-transitory computer-readable medium, such as a compact disc, flashmemory device, random access memory, hard drive, etc. When theinstructions are executed, the processor 1102 carries out the operationsand functions specified in the instructions so as to operate as aspecial-purpose processor that implements the described process(es).Such a processor may be referred to as a “processor circuit” or“processor circuitry” in some examples.

Reference is now also made to FIG. 18, which shows a simplified blockdiagram of an example embodiment of a decoder 1200. The decoder 1200includes a processor 1202, a memory 1204, and a decoding application1206. The decoding application 1206 may include a computer program orapplication stored in memory 1204 and containing instructions that, whenexecuted, cause the processor 1202 to perform operations such as thosedescribed herein. It will be understood that the decoding application1206 may be stored on a computer-readable medium, such as a compactdisc, flash memory device, random access memory, hard drive, etc. Whenthe instructions are executed, the processor 1202 carries out theoperations and functions specified in the instructions so as to operateas a special-purpose processor that implements the describedprocess(es). Such a processor may be referred to as a “processorcircuit” or “processor circuitry” in some examples.

It will be appreciated that the decoder and/or encoder according to thepresent application may be implemented in a number of computing devices,including, without limitation, servers, suitably-programmed generalpurpose computers, machine vision systems, and mobile devices. Thedecoder or encoder may be implemented by way of software containinginstructions for configuring a processor or processors to carry out thefunctions described herein. The software instructions may be stored onany suitable non-transitory computer-readable memory, including CDs,RAM, ROM, Flash memory, etc.

It will be understood that the decoder and/or encoder described hereinand the module, routine, process, thread, or other software componentimplementing the described method/process for configuring the encoder ordecoder may be realized using standard computer programming techniquesand languages. The present application is not limited to particularprocessors, computer languages, computer programming conventions, datastructures, other such implementation details. Those skilled in the artwill recognize that the described processes may be implemented as a partof computer-executable code stored in volatile or non-volatile memory,as part of an application-specific integrated chip (ASIC), etc.

The present application also provides for a computer-readable signalencoding the data produced through application of an encoding process inaccordance with the present application.

Certain adaptations and modifications of the described embodiments canbe made. Therefore, the above discussed embodiments are considered to beillustrative and not restrictive.

What is claimed is:
 1. A method of encoding a point cloud to generate abitstream of compressed point cloud data, the point cloud being locatedwithin a volumetric space containing the points of the point cloud, eachof the points having a geometric location within the volumetric space,wherein a sub-volume within the volumetric space contains a set ofpoints the locations of which are to-be-coded, the method comprising:determining a plurality of candidate coding modes, wherein eachcandidate coding mode transforms a set of previously-coded points into acandidate predicted set of points; selecting a coding mode from amongthe plurality of candidate coding modes using rate-distortionoptimization, where the rate-distortion optimization includes, for oneof the candidate coding modes, determining a geometric distortionbetween the set of points and the candidate predicted set of pointsproduced by said one of the candidate coding modes, and wherein thegeometric distortion is determined based on a sum of the absolutedistance between each point in the set of points and a respectivenearest predicted point in said candidate predicted set of points; andcoding the set of points partly based on the predicted set of pointsdetermined by the selected coding mode, to generate the bitstream. 2.The method claimed in claim 1, wherein the coding mode includes a motionvector defining a translation of the set of previously-coded points togenerate the candidate predicted set of points.
 3. The method claimed inclaim 1, wherein the geometric distortion is determined based on a sumof a non-linear function of the absolute distance between each point andits respective nearest predicted point in said candidate predicted setof points.
 4. The method claimed in claim 1, wherein the geometricdistortion is determined based on a sum of a logarithm of the absolutedistance between each point and its respective nearest predicted pointin said candidate predicted set of points.
 5. The method claimed inclaim 4, wherein the geometric distortion, D, is determined inaccordance with the expression:$D = {\sum\limits_{\beta \in B}{\log_{2}\left( {1 + {\min\limits_{\varphi \in P}{{\beta - \varphi}}_{1}}} \right)}}$where B is the set of points in the volume, β is a point in the set ofpoints in the volume, P is the predicted set of points, and φ is therespective nearest predicted point to the point β in the set of points.6. The method claimed in claim 1, wherein the respective nearestpredicted point to each point in the set of points is determined byfinding, for a particular point in the set of points, a predicted pointin the set of predicted points that has an L1 distance from theparticular point.
 7. The method claimed in claim 1, wherein selecting acoding mode includes performing a multi-round iterative search for alocally-best coding mode within a search range, and wherein eachsuccessive round of the search includes determining two or morelocally-best coding modes and defining successive new search rangescentered around respective points identified by said locally-best codingmodes.
 8. The method claimed in claim 7, wherein the multi-round searchdetermining two or more locally-best coding modes includes calculating,for each candidate coding mode in a particular round, a rate-distortionexpression that includes the geometric distortion attributable to thatcandidate coding mode, and identifying two or more locally least-costcoding modes for that particular round.
 9. The method claimed in claim1, wherein coding the set of points includes context-based entropycoding the set of points using context selection based, at least inpart, on the predicted set of points.
 10. The method claimed in claim 1,wherein the set of previously-coded points are previously-coded pointsfrom the point cloud located in a second volume positioned proximate thevolume.
 11. The method claimed in claim 1, wherein the set ofpreviously-coded points are from a second point cloud temporally-relatedto the point cloud.
 12. The method claimed in claim 1, wherein thevolumetric space is recursively partitioned and one of the partitions isthe sub-volume.
 13. An encoder for encoding a point cloud to generate abitstream of compressed point cloud data, the point cloud being locatedwithin a volumetric space recursively split into sub-volumes andcontaining the points of the point cloud, each of the points having ageometric location within the volumetric space, wherein a volumecontains a set of points the locations of which are to-be-coded, theencoder comprising: a processor; memory; and an encoding applicationcontaining instructions executable by the processor that, when executed,cause the processor to: determine a plurality of candidate coding modes,wherein each candidate coding mode transforms a set of previously-codedpoints into a candidate predicted set of points; select a coding modefrom among the plurality of candidate coding modes using rate-distortionoptimization, where the rate-distortion optimization includes, for oneof the candidate coding modes, determining a geometric distortionbetween the set of points and the candidate predicted set of pointsproduced by said one of the candidate coding modes, and wherein thegeometric distortion is determined based on a sum of the absolutedistance between each point in the set of points and a respectivenearest predicted point in said candidate predicted set of points; andcode the set of points partly based on the predicted set of pointsdetermined by the selected coding mode, to generate the bitstream. 14.The encoder claimed in claim 13, wherein the coding mode includes amotion vector defining a translation of the set of previously-codedpoints to generate the candidate predicted set of points.
 15. Theencoder claimed in claim 13, wherein the geometric distortion isdetermined based on a sum of a non-linear function of the absolutedistance between each point and its respective nearest predicted pointin said candidate predicted set of points.
 16. The encoder claimed inclaim 13, wherein the geometric distortion is determined based on a sumof a logarithm of the absolute distance between each point and itsrespective nearest predicted point in said candidate predicted set ofpoints.
 17. The encoder claimed in claim 16, wherein the geometricdistortion, D, is determined in accordance with the expression:$D = {\sum\limits_{\beta \in B}{\log_{2}\left( {1 + {\min\limits_{\varphi \in P}{{\beta - \varphi}}_{1}}} \right)}}$where B is the set of points in the volume, β is a point in the set ofpoints in the volume, P is the predicted set of points, and φ is therespective nearest predicted point to the point β in the set of points.18. The encoder claimed in claim 13, wherein the respective nearestpredicted point to each point in the set of points is determined byfinding, for a particular point in the set of points, a predicted pointin the set of predicted points that has an L1 distance from theparticular point.
 19. The encoder claimed in claim 13, wherein theinstructions, when executed, are to cause the processor to select acoding mode by performing a multi-round iterative search for alocally-best coding mode within a search range, and wherein eachsuccessive round of the search includes determining two or morelocally-best coding modes and defining successive new search rangescentered around respective points identified by said locally-best codingmodes.
 20. A non-transitory processor-readable medium storingprocessor-executable instructions for encoding a point cloud to generatea bitstream of compressed point cloud data, the point cloud beinglocated within a volumetric space containing the points of the pointcloud, each of the points having a geometric location within thevolumetric space, wherein a sub-volume within the volumetric spacecontains a set of points the locations of which are to-be-coded, whereinthe instructions, when executed by a processor, cause the processor to:determine a plurality of candidate coding modes, wherein each candidatecoding mode transforms a set of previously-coded points into a candidatepredicted set of points; select a coding mode from among the pluralityof candidate coding modes using rate-distortion optimization, where therate-distortion optimization includes, for one of the candidate codingmodes, determining a geometric distortion between the set of points andthe candidate predicted set of points produced by said one of thecandidate coding modes, and wherein the geometric distortion isdetermined based on a sum of the absolute distance between each point inthe set of points and a respective nearest predicted point in saidcandidate predicted set of points; and code the set of points partlybased on the predicted set of points determined by the selected codingmode, to generate the bitstream.